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number-of-beautiful-integers-in-the-range.py
138 lines (125 loc) · 5.76 KB
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number-of-beautiful-integers-in-the-range.py
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# Time: O(n^2 * k), n = len(str(high))
# Space: O(n^2 * k)
# memoization (faster but more space)
class Solution(object):
def numberOfBeautifulIntegers(self, low, high, k):
"""
:type low: int
:type high: int
:type k: int
:rtype: int
"""
TIGHT, UNTIGHT, UNBOUND = range(3)
def f(x):
digits = map(int, str(x))
lookup = [[[[-1]*k for _ in xrange(2*len(digits)+1)] for _ in xrange(3)] for _ in xrange(len(digits))]
def memoization(i, state, diff, total):
if i == len(digits):
return int(state != UNBOUND and diff == total == 0)
if lookup[i][state][diff][total] == -1:
result = int(i != 0 and diff == total == 0) # count if the beautiful integer x s.t. len(str(x)) < len(digits)
for d in xrange(1 if i == 0 else 0, 10):
new_state = state
if state == TIGHT and d != digits[i]:
new_state = UNTIGHT if d < digits[i] else UNBOUND
new_diff = diff+(1 if d%2 == 0 else -1)
new_total = (total*10+d)%k
result += memoization(i+1, new_state, new_diff, new_total)
lookup[i][state][diff][total] = result
return lookup[i][state][diff][total]
return memoization(0, TIGHT, 0, 0)
return f(high)-f(low-1)
# Time: O(n^2 * k), n = len(str(high))
# Space: O(n * k)
# dp (slower but less space)
class Solution2(object):
def numberOfBeautifulIntegers(self, low, high, k):
"""
:type low: int
:type high: int
:type k: int
:rtype: int
"""
TIGHT, UNTIGHT, UNBOUND = range(3)
def f(x):
digits = map(int, str(x))
dp = [[[0]*k for _ in xrange(2*len(digits)+1)] for _ in xrange(3)]
for tight in xrange(2):
for state in (TIGHT, UNTIGHT):
dp[state][0][0] = 1
for i in reversed(xrange(len(digits))):
new_dp = [[[0]*k for _ in xrange(2*len(digits)+1)] for _ in xrange(3)]
for state in (TIGHT, UNTIGHT, UNBOUND):
new_dp[state][0][0] = int(i != 0) # count if the beautiful integer x s.t. len(str(x)) < len(digits)
for d in xrange(1 if i == 0 else 0, 10):
new_state = state
if state == TIGHT and d != digits[i]:
new_state = UNTIGHT if d < digits[i] else UNBOUND
for diff in xrange(-len(digits), len(digits)+1):
new_diff = diff+(1 if d%2 == 0 else -1)
for total in xrange(k):
new_total = (total*10+d)%k
new_dp[state][diff][total] += dp[new_state][new_diff][new_total]
dp = new_dp
return dp[TIGHT][0][0]
return f(high)-f(low-1)
# Time: O(n^2 * k), n = len(str(high))
# Space: O(n^2 * k)
# memoization (faster but more space)
class Solution3(object):
def numberOfBeautifulIntegers(self, low, high, k):
"""
:type low: int
:type high: int
:type k: int
:rtype: int
"""
def f(x):
digits = map(int, str(x))
lookup = [[[[[-1]*k for _ in xrange(2*len(digits)+1)] for _ in xrange(2)] for _ in xrange(2)] for _ in xrange(len(digits))]
def memoization(i, zero, tight, diff, total):
if i == len(digits):
return int(zero == diff == total == 0)
if lookup[i][zero][tight][diff][total] == -1:
result = 0
for d in xrange((digits[i] if tight else 9)+1):
new_zero = int(zero and d == 0)
new_tight = int(tight and d == digits[i])
new_diff = diff+((1 if d%2 == 0 else -1) if new_zero == 0 else 0)
new_total = (total*10+d)%k
result += memoization(i+1, new_zero, new_tight, new_diff, new_total)
lookup[i][zero][tight][diff][total] = result
return lookup[i][zero][tight][diff][total]
return memoization(0, 1, 1, 0, 0)
return f(high)-f(low-1)
# Time: O(n^2 * k), n = len(str(high))
# Space: O(n * k)
# dp (slower but less space)
class Solution4(object):
def numberOfBeautifulIntegers(self, low, high, k):
"""
:type low: int
:type high: int
:type k: int
:rtype: int
"""
def f(x):
digits = map(int, str(x))
dp = [[[[0]*k for _ in xrange(2*len(digits)+1)] for _ in xrange(2)] for _ in xrange(2)]
for tight in xrange(2):
dp[0][tight][0][0] = 1
for i in reversed(xrange(len(digits))):
new_dp = [[[[0]*k for _ in xrange(2*len(digits)+1)] for _ in xrange(2)] for _ in xrange(2)]
for zero in xrange(2):
for tight in xrange(2):
for d in xrange((digits[i] if tight else 9)+1):
new_zero = int(zero and d == 0)
new_tight = int(tight and d == digits[i])
for diff in xrange(-len(digits), len(digits)+1):
new_diff = diff+((1 if d%2 == 0 else -1) if new_zero == 0 else 0)
for total in xrange(k):
new_total = (total*10+d)%k
new_dp[zero][tight][diff][total] += dp[new_zero][new_tight][new_diff][new_total]
dp = new_dp
return dp[1][1][0][0]
return f(high)-f(low-1)